this will

• recode for \#steps \in [10, 20, 100]
• at t = 0, k random shards among the n encoded will be selected at random
• at t \geq 1, all k shards will be used to recode k brand new shards
• make sure the last set of k shards recoded \#steps together can decode the data

example with (k, n) = (3, 5) and \#steps = 3

• (s_i)_{1 \leq i \leq k} are the k source shards
• (e_j)_{1 \leq j \leq n} are the n encoded shards
• (m_i)_{1 \leq i \leq k} are the k randomly selected shards
• (n_i)_{1 \leq i \leq k} are the shards after step 1
• (o_i)_{1 \leq i \leq k} are the shards after step 2
• (p_i)_{1 \leq i \leq k} are the shards after step 3
• the (p_i)_{1 \leq i \leq k} will be used for decoding

graph TD;

    s1 --> e1; s1 --> e2; s1 --> e3; s1 --> e4; s1 --> e5;
    s2 --> e1; s2 --> e2; s2 --> e3; s2 --> e4; s2 --> e5;
    s3 --> e1; s3 --> e2; s3 --> e3; s3 --> e4; s3 --> e5;

    e1 --> m1;
    e3 --> m2;
    e4 --> m3;

    m1 --> n1; m1 --> n2; m1 --> n3;
    m2 --> n1; m2 --> n2; m2 --> n3;
    m3 --> n1; m3 --> n2; m3 --> n3;

    n1 --> o1; n1 --> o2; n1 --> o3;
    n2 --> o1; n2 --> o2; n2 --> o3;
    n3 --> o1; n3 --> o2; n3 --> o3;

    o1 --> p1; o1 --> p2; o1 --> p3;
    o2 --> p1; o2 --> p2; o2 --> p3;
    o3 --> p1; o3 --> p2; o3 --> p3;